When my pampas grass begins to plume the birds take the plumes

I've had this in a garden for 20 years, but I'm curious about what you're saying - the plumes appear usually in September or October, and persist over the winter (getting increasingly tatty, of course) and its in the early part of the year, say late January at the earliest, more usually Feb/Mar, that the birds start taking the remains of the plumes. In fact, I used to leave them on the plant to allow them to do this, even though they looked very tatty after the winter.
Birds don't build nests in autumn - are you saying they take the plumes as soon as they appear, or later?

I've just realised you're in the States - I don't know when they flower where you live, but surely it must be the early Fall?

you could use flees but it would look ugly .i think let nature do its thing or perhaps and its only a perhaps put something out thats natural that the birds would prefer like old sheeps wool .personaly id enjoy watching the birds do what nature intended them to do but hay ho